ALEC has long been a target for liberal groups, and has come under intense scrutiny over the past few weeks over its support of NRA-backed "Stand Your Ground" legislation that enhances citizens' ability to claim self-defense to avoid prosecution for harming or killing someone.

The Sanford, Fla., police department originally said it couldn't legally arrest Martin's shooter, George Zimmerman, because of the state's "Stand Your Ground" law. However, the state of Florida arrested Zimmerman on Wednesday and charged him with second-degree murder, which carries a maximum sentence of life in prison.

Update: This post was updated at 8:20 p.m. to reflect that Blue Cross Blue Shield says its decision not to renew its membership with ALEC was made independently of the Trayvon Martin case.